System and method for optimizing image resolution using pixelated imaging devices

ABSTRACT

A method of processing image data for display on a pixelated imaging device is disclosed. The method comprises: pre-compensation filtering an image input to produce pre-compensation filtered pixel values, the pre-compensation filter having a transfer function that approximates the function that equals one divided by a pixel transfer function; and displaying the pre-compensation filtered pixel values on the pixelated imaging device.  
     In another disclosed method, the method further comprises: pre-compensation filtering an image input for each of a plurality of superposed pixelated imaging devices, at least two of which are unaligned, to produce multiple sets of pre-compensation filtered pixel values; and displaying the multiple pre-compensation filtered pixel values on the plurality of superposed pixelated imaging devices.

CROSS-REFERENCE TO RELATED APPLICATION

[0001] This application claims the benefit of our provisionalapplication serial number 60/179,762, filed Feb. 2,2000, the disclosureof which is hereby incorporated herein by reference.

FIELD OF THE INVENTION

[0002] The invention generally relates to systems and methods foroptimizing the resolution of graphical displays, and more particularlythe invention relates to systems and methods for optimizing theresolution of pixelated displays.

BACKGROUND OF THE INVENTION

[0003] Graphical display engineers continue to minimize pixel hardwaresize. However, for any given minimum pixel size, there is an ongoingneed to optimize display resolution.

SUMMARY OF THE INVENTION

[0004] In one embodiment of the invention, a method of processing imagedata for display on a pixelated imaging device comprises:pre-compensation filtering an image input to produce pre-compensationfiltered pixel values, the pre-compensation filter having a transferfunction that approximates the function that equals one divided by apixel transfer function; and displaying the pre-compensation filteredpixel values on the pixelated imaging device.

[0005] In another embodiment of the invention, a method furthercomprises: pre-compensation filtering an image input for each of aplurality of superposed pixelated imaging devices, at least two of whichare unaligned, to produce multiple sets of pre-compensation filteredpixel values; and displaying the multiple pre-compensation filteredpixel values on the plurality of superposed pixelated imaging devices.

[0006] In a further embodiment of the invention, a method furthercomprises: displaying the multiple pre-compensation filtered pixelvalues on six imagers, the six imagers being positioned into four phasefamilies, the first and third phase families corresponding to separategreen imagers, the second and fourth phase families corresponding toseparate sets of aligned blue and red imagers.

[0007] Further related system and method embodiments are also disclosed.

BRIEF DESCRIPTION OF THE DRAWINGS

[0008] The foregoing description of various embodiments of the inventionshould be appreciated more fully from the following further descriptionthereof with reference to the accompanying drawings wherein:

[0009]FIG. 1 shows an imager arrangement for optimizing displayresolution in accordance with an embodiment of the invention;

[0010]FIGS. 2A and 2B show schematic block diagrams of methods ofprocessing image signals to optimize image resolution, in accordancewith two different embodiments of the invention;

[0011]FIGS. 3A and 3B detail implementation of pre-compensation filtersin accordance with two different embodiments of the invention;

[0012]FIG. 4 shows a one-dimensional pixel transfer function;

[0013]FIG. 5 shows a set of transfer functions, determined in accordancewith an embodiment of the invention;

[0014]FIG. 6 shows a two-dimensional pixel transfer function;

[0015]FIG. 7 shows a two-dimensional pre-compensated pixel transferfunction, determined in accordance with an embodiment of the invention;

[0016]FIG. 8 shows an extended pre-compensation filter tranfer function,in accordance with an embodiment of the invention; and

[0017]FIG. 9 shows a set of multiple unaligned imagers for optimizingimage appearance to the human eye, in accordance with an embodiment ofthe invention.

DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS

[0018]FIG. 1 shows an imager arrangement for optimizing displayresolution in accordance with an embodiment of the invention. Each ofpixelatled imaging devices 101-104 includes pixel hardware that forms anarray of regular polygons, tiling a planar area. To optimize displayresolution, multiple pixelated imaging devices 101-104 are superposed inan unaligned fashion, to form a combined display device 109. Eachsuccessive imaging device of the four superposed imaging devices 101-104is offset by one-quarter of the pixel dimension S, in both the verticaland horizontal directions.

[0019] Individual pixel-like features 111 of the resulting combineddisplay device 109 have a minimum dimension, S/4, that is one-quarterthe minimum dimension, S, of the actual pixels of each separate imagingdevice 101-104. The pixel-like features 111 of the combined displaydevice 109 thus have a square area that is one-sixteenth that of theactual pixels of each separate imaging device 101-104. The sizereduction may be seen in FIG. 1 by comparing the size of individualpixel-like feature 110 of the combined display device 109, with the sizeof individual pixels 105-108 of the separate pixelated imaging devices101-104.

[0020] The unaligned superposition of FIG. 1 thus allows increaseddisplay resolution for a given minimum pixel dimension S, which may, forexample, be the smallest pixel dimension that is presently capable ofbeing implemented in hardware for a single separate display.

[0021] In FIG. 1, the polygons of imaging devices 101-104 are square,but they may also be rectangular, or any other shape, in accordance withan embodiment of the invention. While four pixelated imaging devices areshown in FIG. 1, any number may be used. In addition, the lack ofalignment of the separate imaging devices may be produced by a varietyof different methods, in accordance with other embodiments of theinvention. For example, pixelated imaging devices with square orrectangular pixels may be spatially shifted by a different amount in thehorizontal direction than in the vertical direction. Two or more imagingdevices may be aligned with each other, with no spatial shift, whileothers are unaligned with each other, in the same display. A lack ofalignment may also be produced by an optical or physical change betweenthe separate imaging devices; or by changing the separate imagingdevices' scale, rotational angle, aspect ratio, or liner offset withrespect to each other. In another embodiment, a time-multiplexed imagermay be used to produce the same effect as is produced by superposingmultiple separate imaging devices: the imager or optics of thetime-multiplexing imager moves to a different position when transmittinga signal that corresponds to each of the separate imaging devices.

[0022] The below chart shows a comparison of three displays: in the“Aligned” array, three pixelated imagers are fully aligned, with nooffset as shown in FIG. 1. In the “½ offset” array, three imagers areused, one having green color information, and the other two having blueand red information; the blue and red arrays are aligned with eachother, but both diagonally offset by ½ of the pixel diagonal spacingfrom the green imager. In the “¼ offset” array, six imagers are used,two for red information, two for green, and two for blue, as will befurther described below in connection with FIG. 9. The comparison showsthe increase in effective resolution, and decrease in imager visibility,that results from un-aligning superposed imagers, as in the embodimentof FIG. 1: Aligned ½ offset ¼ offset Array Size 1280 × 1024 × 3 1280 ×1024 × 3 1280 × 1024 × 6 Hor. 1280 1280 × 2 1280 × 4 Addressable Vert.1024 1024 × 2 1024 × 4 Addressable Effective 1280 × 1024 1800 × 14002560 × 2048 Resolution Imager 1 ½ ¼ visibility

[0023] In the above table, “Imager Visibility” is used to refer to therelative visibility of the imager as compared with the image whenviewing the image of a close distance. As can be seen, unaligned imagersreduce the imager visibility, which is caused by the imagers' finiteresolution and interpixel gaps; in general the reduction of imagervisibility is proportional to the number of offsets used.

[0024]FIGS. 2A and 2B show schematic block diagrams of methods ofprocessing image signals to optimize image resolution, in accordancewith two different embodiments of the invention. In a pixelated griddisplay, frequency response tapers off to zero at the Nyquist frequencyof the 2D box filter implemented by the filter. This response variesaccording to radial frequency direction, and phase relationship to thepixel grid. To improve the image quality achieved by such a pixelateddisplay, an embodiment according to the invention oversamples an imagerelative to the display, and generates pixel values by using a two- orthree-dimensional pre-compensation filter. The filter combines radialbandlimiting, to avoid aliasing, with pre-compensation for the imperfectand directional frequency response function of the display.

[0025] In step 221 of FIG. 2A, an image input is fed to apre-compensation filter. The image input may be in any of a variety offormats, including, for example, HDTV, NTSC, PAL etc. In step 222 ofFIG. 2A, the pre-compensation filter transforms the image input andfeeds the resulting output directly to a pixelated imaging device, wherean image is displayed in step 223. In the embodiment of FIG. 2A, thepixelated imaging device may be a conventional display, so that thepre-compensation filter improves the sharpness and resolution of aconventional display in a fashion described further below.

[0026] By contrast, in step 225 of the embodiment of FIG. 2B, thepre-compensation filter transforms the image input into a set ofpre-compensated image signals, and feeds each pre-compensated signal toa different imaging device of a combined set of superposed, unalignedpixelated imaging devices. For example, the pre-compensation filter mayfeed a separate pre-compensated output signal to each of the imagingdevices 101-104 that form the combined pixelated imaging device 109 ofthe embodiment of FIG. 1. In step 226 of FIG. 2B, a resulting image isdisplayed on the combined set of superposed, unaligned pixelated imagingdevices.

[0027]FIGS. 3A and 3B further detail implementation of pre-compensationfilters in accordance with two different embodiments of the invention.The filters may be used, for example, as pre-compensation filters in theembodiments of FIGS. 2A and 2B, respectively.

[0028] In step 331 of FIG. 3A, the transfer function of an individualpixel is determined. This may be performed by determining the FourierTransform (or other frequency-domain representation) of the pixel'simpulse response.

[0029] For example, a pixel could be modeled in one dimension as havinga “boxcar” impulse response, equal to 1 at the pixel's spatial locationand 0 elsewhere. A transfer function for such a pixel is given by:$\begin{matrix}{{H\lbrack x\rbrack} = {{{Sinc}\lbrack x\rbrack} = \left\{ \begin{matrix}{1,{x = 0}} \\{\frac{\sin \lbrack x\rbrack}{x},{x \neq 0}}\end{matrix} \right.}} & \left\{ {{Eq}.\quad 1} \right\}\end{matrix}$

[0030] for spatial frequency x. This transfer function is shown in thegraph of FIG. 4, with frequency x on the x-axis in radians, and thepixel's transfer function on the y-axis.

[0031] Analogously, a pixel could be modeled in two dimensions as asquare finite impulse response filter with unity coefficients inside thepixel's spatial location and zero coefficients elsewhere. A transferfunction for such a pixel is given by:

H[u,V]=Sinc[u]* Sinc[V]  {Eq.2}

[0032] with Sinc as defined for Equation 1, and “*” denotingconvolution.

[0033] Next, in step 332 of FIG. 3A, the pixel's transfer function isused to determine a transfer function for the pre-compensation filter.In one embodiment according to the invention, the pre-compensationfilter is chosen such that its transfer function satisfies theexpression:

{Pre-compensation filter transfer function}={1/pixel transferfunction}  {Eq. 3}

[0034] although other relations that give similar results will beapparent to those of ordinary skill in the art.

[0035] Next, in step 333 of FIG. 3A, an adjusted transfer function forthe pre-compensation filter is determined. This step may involve, forexample, gain-limiting the pre-compensation filter's transfer function;or clipping off its values at aliasing frequencies. For example, usingthe one-dimensional example above, an example of a gain-limited andclipped pre-compensation filter transfer function is given by:$\begin{matrix}{{H_{G}\lbrack x\rbrack} = \left\{ \begin{matrix}{0,{{{{Abs}\lbrack x\rbrack} > \pi};}} \\{{{{Sign}\left\lbrack {{Sinc}\lbrack x\rbrack} \right\rbrack}\left( {G - {\left( {\left( {G/2} \right)\hat{}2} \right){{abs}\left\lbrack {{Sinc}\lbrack x\rbrack} \right\rbrack}}} \right\}},{{{{Abs}\left\lbrack {{Sinc}\lbrack x\rbrack} \right\rbrack} < {2/G}};}} \\{{1/{{Sinc}\lbrack x\rbrack}},{otherwise}}\end{matrix} \right.} & \left\{ {{Eq}.\quad 4} \right\}\end{matrix}$

[0036] with G being a gain factor that could be set, for example, toequal 4.

[0037] Using the analogous two-dimensional example given above, anexample of a two-dimensional gain-limited and clipped pre-compensationfilter transfer function is given by: $\begin{matrix}{{H_{G}\left\lbrack {u,V} \right\rbrack} = \left\{ \begin{matrix}{0,{{{{Abs}\lbrack u\rbrack} > \pi};}} \\{0,{{{{Abs}\lbrack V\rbrack} > \pi};}} \\{{{Sign}\left\lbrack {{{Sinc}\lbrack u\rbrack}*{{Sinc}\lbrack v\rbrack}} \right\rbrack}\left( {{G - {\left( {\left( {G/2} \right)\hat{}2} \right){{Abs}\left\lbrack {{{Sinc}\lbrack u\rbrack}*{{Sinc}\lbrack V\rbrack}} \right)}}},} \right.} \\{{{\_ \quad \_ \quad \_ \quad \_ \quad \_ \quad {for}\quad \_ \quad {{Abs}\left\lbrack {{{Sinc}\lbrack u\rbrack}*{{Sinc}\lbrack V\rbrack}} \right\rbrack}} < {2/G}};} \\{{1/\left( {{{Sinc}\lbrack u\rbrack}*{{Sinc}\lbrack V\rbrack}} \right)},{otherwise}}\end{matrix} \right.} & \left\{ {{Eq}.\quad 5} \right\}\end{matrix}$

[0038] with G being a gain factor that could be set, for example, toequal 4.

[0039] Next, in step 334 of FIG. 3A, the adjusted transfer function ofthe pre-compensation filter calculated in step 333 is used to calculateindividual coefficients of a pre-compensation finite impulse responsefilter. This is performed by a transform back into the spatial domain(out of the frequency domain), using, for example, an inverse Fouriertransform. In the two-dimensional example given above, an individualpre-compensation filter coefficient can be calculated by the expression:$\begin{matrix}{{C\left\lbrack {m,n} \right\rbrack} = {\frac{1}{\pi\hat{}2}{\int_{0}^{\pi}{\int_{0}^{\pi}{{H_{G}\left\lbrack {u,V} \right\rbrack}{\cos \lbrack{mu}\rbrack}{\cos \lbrack{nV}\rbrack}{u}{V}}}}}} & \left\{ {{Eq}.\quad 6} \right\}\end{matrix}$

[0040] Next, in step 335 of FIG. 3A, the entire pre-compensation finiteimpulse response filter is determined, by combining individualcoefficients as calculated in step 334 into a single array formed fromcoefficients that correspond to each pixel location in the display.Thus, for example, Equation 6 could be used to calculate a coefficientfor each pair (m,n) of a coordinate system covering a two-dimensionalpixelated imaging device.

[0041] Next, in step 336 of FIG. 3A, the pre-compensation finite impulseresponse filter determined in step 335 is used to transform image inputdata; and, in step 337, the resulting filtered image is displayed.

[0042] In this fashion a pre-compensation filter of the embodiment ofFIG. 3A may be used to improve the resolution of a pixelated imagingdevice, which may be, for example, a conventional pixelated display. Theimprovement in image appearance is evidenced by FIG. 5, which shows agraph of transfer functions in accordance with the one-dimensionalexample used above. The pixel transfer function H[x] 550 is plotted onthe same axes as the transfer function 552 of the pre-compensationfinite impulse response filter formed from coefficients C[m,n]. Transferfunction 551 is the pre-compensated pixel transfer function that resultsfrom transforming an image input with the pre-compensation filter beforefeeding it to the pixelated display. The more “square-shouldered”transfer function 551 of the pre-compensated display, as compared withthe rounded transfer function 550 of the display withoutpre-compensation, is evidence of the improved resolution brought aboutby the embodiment of FIG. 3A. A similar contrast may be observed bycomparing the shape of the two-dimensional pixel transfer function of adisplay that lacks pre-compensation (FIG. 6) with the“square-shouldered” pixel transfer function of a pre-compensated display(FIG. 7).

[0043] In an alternative version of the embodiment of FIG. 3A, thepre-compensation filter need not be “clipped off” within the frequencyband shown above; instead, it may have an extended frequency range. FIG.8 shows a pixel transfer function 801, an extended pre-compensationfilter transfer function 802, and the “square-shouldered” transferfunction 803 that results from using the pre-compensation filter 802 tofilter image input.

[0044] Whereas the embodiment of FIG. 3A may be used with a singlepixelated imaging device, the embodiment of FIG. 3B may be used withmultiple, superposed imaging devices, such as the unaligned imagingdevices of the embodiment of FIG. 1.

[0045] Steps 338-340 of FIG. 3B mirror steps 331-333 of FIG. 3A. In step341 of FIG. 3B, however, individual coefficients of pre-compensationfilters are calculated in a similar fashion to that of step 334 of FIG.3A, but by also taking into consideration the spatial phase shift of theunaligned imagers to which the filters correspond. For example, a set offour pre-compensation filters would be used to filter inputs to the fourunaligned imagers 101-104 of the embodiment of FIG. 1, with onepre-compensation filter corresponding to each one of the imagers101-104. When calculating coefficients for the pre-compensation filterfor imager 101, a phase-shift of zero would be included; but whencalculating coefficients for the filter for imager 102, a diagonalphase-shift of one-quarter of a pixel would be included in thecalculations; and so on. In the expression of Equation 6, for example,having the values of m and n both range from −3¾ to +4 ¼ could be usedto calculate coefficients of a filter corresponding to a one-quarterdiagonal pixel offset imager; as compared with ranges from −4 to +4 foran imager with zero diagonal offset, and −3 ½ to +4 ½ for an imager witha one-half diagonal pixel offset.

[0046] In step 342, the individual coefficients calculated in step 341are used to calculate an entire pre-compensation finite impulse responsefilter, for each spatially phase-shifted pixelated imaging device. Arrow343 indicates that individual coefficients are calculated, in step 341,until the coefficients for all pre-compensation filters are filled. Forexample, four filter arrays would be filled with coefficients, to createfour pre-compensation filters for the unaligned imagers of theembodiment of FIG. 1.

[0047] In step 344, each pre-compensation filter is used to transformimage input data for its corresponding phase-shifted pixelated imagingdevice. In step 345, a superposed, pre-compensation filtered image isdisplayed.

[0048]FIG. 9 shows a method in accordance with an embodiment of theinvention that optimizes image resolution by adapting the previouslydescribed methods to the human eye's optics. The eye's perception of Redand Green is ⅓ its perception of luminance, and its perception of Blueand Yellow is ⅛ its perception of luminance. Thus, high-frequencyinformation in the luminance component of an image is more valuable thaninformation in the chrominance components, for optimizing an image'sappearance.

[0049] The embodiment of FIG. 9 uses a set of six superposed, unalignedimagers to take into account these aspects of the eye's perception. Twoimagers are fed red chrominance information, two are fed greenchrominance information, and two are fed blue chrominance information.Because of the eye's different weighting of different colors, the siximagers are combined into four phase families: a first, single greenimager 901 has zero phase offset; a second imager 902 comprising a blueimager aligned with a red imager has a ¼ diagonal pixel offset ascompared with the single green imager 901; a third imager 903 comprisinga single green imager has a ½ diagonal pixel offset as compared with thesingle green imager 901; and a fourth imager 904 comprising a blueimager aligned with a red imager has a ¾ diagonal pixel offset ascompared with the single green imager 901.

[0050] The embodiment of FIG. 9 may be operated in a similar fashion tothat described in FIGS. 2B and 3B, or may be fed phase-shifted signalswithout pre-compensation.

[0051] In another embodiment according to the invention, aperception-based representation of the image—such as a YUV or HISrepresentation, for example, instead of an RGB representation—isprocessed by its own reconstruction filter. The output of the filteryields the appropriate perception-based pixel value for each element ofeach grid; this is then converted to the appropriate color value foreach element of each grid.

[0052] While the embodiments described above have been discussed interms of image projection on pixelated displays, similar methods may beused for image sensing and recording, in accordance with an embodimentof the invention.

[0053] Multiple unaligned sensors may be set up, in an analogous fashionto the multiple displays of FIG. 1; or one image may be split amongmultiple real or time-multiplexed imagers by beam splitters.

[0054] For color applications, each imager may operate in one colorfrequency band. For example, a set of six unaligned color sensors may beimplemented in a similar fashion to that described for FIG. 9. As withthe embodiments of FIGS. 2B and 3B, the image inputs from each sensordevice may be pre-compensation filtered.

[0055] In addition, however, the separate viewpoint provided by eachsensor may be considered as a single 2D-filtered view of an infinitenumber of possible image signals, that provides constraints on the imageto be displayed. A, displayed image is then calculated by determiningthe lowest energy signal that satisfies the constraints established bythe signals from the various separate sensors. That is, the energy$\begin{matrix}{\sum\limits_{m}{\sum\limits_{n}{{{Abs}\left\lbrack {S\quad\left\lbrack {m,n} \right\rbrack} \right\rbrack}\bigwedge 2}}} & \text{\{Eq.7\}}\end{matrix}$

[0056] is minimized for proposed signals S[m,n] that satisfy theboundary conditions established by sensor image signals S₁[m,n] . . .S_(k)[m,n], for k imagers. The proposed signal S[m,n] that provides theminimum energy value is then used as the sensed signal for display.

[0057] In another embodiment, a color camera is implemented b, dividingthe visible spectrum for each physical sensor using a diachroic prism.In one example, six imagers are used, with a prism dividing the imageinto six color frequency ranges. Information from each color frequencyrange is then supplied to a displaced imager. The lowest energyluminance and color difference signals are then solved. These signalssatisfy the constraints generated by the six imager signals and theirknown 2D frequency response and phasing. In addition to the frequencyresponse and phasing of each imager, the sagital and tangentialfrequency response of the optics at that light frequency may be includedin calculations, to correct for the Modular Transfer Function (MTF) ofthe optics.

[0058] The contribution of each of the six color bands is then weightedfor human perception of luminance and of the Cb and Cr signals.

[0059] In another embodiment, a playback device is implemented. Theplayback device filters and interpolates the original signal to providethe correct transfer function and signal value at the location of eachpixel on each imager. If more than one imager is used for each colorcomponent, the component image energy may be divided and weighted forperception among the imagers. If each color component is divided intoseparate color frequencies, the image energy may be divided among thosecomponents and weighted by perception.

[0060] Another embodiment comprises a recording device. To record thesignal, there are two approaches. One is to record each imager'sinformation as a separate component. This preserves all of theinformation. The other alternative is to record a combinedhigh-frequency luminance signal and two combined color differencesignals. If three to six imagers are used, good results c(an be obtainedby recording a luminance signal with twice the resolution in bothdimensions as the two color difference signals.

[0061] In a polarized light embodiment, multiple imagers are operatedwith two clases of polarized light. Separate eye views are supplied toimagers, so that a single projection device gives a three-dimensionalappearance to the projected image.

[0062] An embodiment of the invention also provides a technique formanufacturing imagers for use with the embodiments described above. Inaccordance with this embodiment, if color component imagers areassembled with little concern to their precise orientation, or response,spot response sensors (for projection), or calibrated spot generators(in the case of a camera), allow inspection at the geometric extremes ofthe image. This inspection, combined with a hyperaccuity-based signalprocessing approach, determine exact placement phase, scale, rotationand tilt of each manufactured display. If tilt is not required, twosensors suffice.

[0063] In one embodiment, such sensors can be used in manufacturing toset placement parameters. In another embodiment, such sensors are usedin the product to automatically optimize response for component gridplacement. In this embodiment, the sensors can also be used forautomatic color correction and white balance for the currentenvironment. The process and the feedback hardware required can begeneralized to compensate for manufacturing tolerance, operational, orcalibration requirements. In the most general case, automaticcompensation requires a full image sensor for a projector, or areference image generator for a camera. In this case, flat field, blackfield, linearity, color shift, geometric distortion, and modulatedtransfer function can all be compensated for.

[0064] Some embodiments of the invention may be implemented, at least inpart, in any conventional computer programming language comprisingcomputer program code. For example, preferred embodiments may beimplemented, at least in part, in a procedural programming language(e.g., “C”) or an object oriented programming language (e.g., “C++”).Alternative embodiments of the invention may be implemented, at least inpart, as preprogrammed hardware elements (e.g., application specificintegrated circuits, FPGAs, and digital signal processors), or otherrelated components.

[0065] The present invention may be embodied in other specific formswithout departing from the true scope of the invention. The describedembodiments are to be considered in all respects only as illustrativeand not restrictive.

I claim:
 1. A method of processing image data for display on a pixelatedimaging device, the method comprising: pre-compensation filtering animage input to produce pre-compensation filtered pixel values, thepre-compensation filter having a transfer function that approximates thefunction that equals one divided by a pixel transfer function; anddisplaying the pre-compensation filtered pixel values on the pixelatedimaging device.
 2. A method according to claim 1 , in which the methodfurther comprises: pre-compensation filtering an image input for each ofa plurality of superposed pixelated imaging devices, at least two ofwhich are unaligned, to produce multiple sets of pre-compensationfiltered pixel values; and displaying the multiple pre-compensationfiltered pixel values on the plurality of superposed pixelated imagingdevices.
 3. A method according to claim 2 , in which the method furthercomprises: displaying the multiple pre-compensation filtered pixelvalues on six imagers, the six imagers being positioned into four phasefamilies, the first and third phase families corresponding to separategreen imagers, the second and fourth phase families corresponding toseparate sets of aligned blue and red imagers.